Problem: Diana is three years younger than Eduardo. Eduardo is four years older than Chad. Faye is three years older than Chad. Diana is 14 years old. How many years old is Faye?
Solution: Let $C$, $D$, $E$, and $F$ denote the ages of Chad, Diana, Eduardo, and Faye.  We are given three equations. \begin{align*}
D&=E-3 \\
E&=C+4 \\
C+3&=F
\end{align*} Summing these three equations, we find that $E$ and $C$ cancel to leave $D+3=F+1$, which implies $F=D+2$.  Since $D=14$, we have $F=\boxed{16}$.